An Efficient Fuzzy System for Complex Query Answering on Knowledge Graphs

Complex Query Answering (CQA) on knowledge graphs is a fundamental yet challenging task, which can be formalized as answering a subset of first-order logic queries containing logical conjunction, disjunction, negation, and existential quantifiers. Recent research reveals that Link Predictors (LPs) trained on 1-hop queries can generalize to various types of complex queries. However, existing methods neglect crucial characteristics of LPs' outputs, including the effects of highly relevant entities and uncertainty. What's worse, as they model logical operations by fuzzy set operations, these methods suffer from problems like inflexibility, sensitivity to noise, and inconsistency with priority in human cognition, which limits their performance, especially on queries with negation. To address these challenges, we propose an efficient fuzzy system for CQA that requires no extra training overheads and is plug-and-play with existing LP-based methods. Firstly, we expand the output of LPs by two complementary membership functions of weak and strong relevance, which help to distinguish the target entities from highly relevant and irrelevant entities. Subsequently, we model logical operations through fuzzy rule bases and infer the final predictions via defuzzification, providing a flexible and tractable scheme for modeling logical operations. Finally, the effectiveness of the proposed fuzzy system is validated by its outstanding performance on benchmark datasets when compared to state-of-theart methods. The source code of our proposed method is available at https://anonymous.4open.science/r/FuzzSys-CQA-E285.